Tangents

Definition - Tangents Ray BC is tangent to circle A, because the line containing BC intersects the circle in exactly one point. This point is called the point of tangency.

Theorem If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Example 1 – Tangent Lines

Example 2 – Tangent Lines

Theorem – The converse is also true If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

Example 3 – Showing Tangency

Example 4 – Non Tangent Segment

Example 5 Determine if the segments are tangent to the respective circles

CW Tangent Lines of Circles

Theorem If two segments from the same exterior point are tangent to a circle, then they are congruent.

Example 1

Example 2 – Circumscribed Triangles & Perimeter